Marty has been hired by Lone Pine, a high-end department store, to conduct some research. He

is currently modelling the number of customers that enter the store during business hours.

Marty believes that the number of customers that enters the store within an hour can be modelled as a Poisson process with parameter = 5. Assuming Martys model is correct, answer the following questions.

a) In a typical business day, the store is open for 8 hours. How many customers are expected to enter the store on a typical business day?

b) Lone Pine has just opened its doors for today. What is the expected amount of time until the first customer of the day enters the store? Give your answer in terms of hours, minutes, and seconds (as appropriate).

c) For the scenario described in part b), state the distribution for the random variable representing the amount of time, measured in minutes, that Lone Pine would have to wait until the first customer of the day enters the store. Include the values of any parameters for that distribution.

d) What is the probability that in any given 1-hour period, there are no more than 3 customers that enter the store?

Marty is now conducting a different study regarding the number of people that end up purchasing from Lone Pine. He believes that any customer entering the store has a 40% chance of making a purchase, and he also believes that an individual customers decision to make a purchase (or not) is independent of any other customers decisions.

e) There are currently 6 customers in Lone Pine. Assuming Martys assumptions hold true, what is the probability that at least 4 of these 6 customers make a purchase?